Praise be to Allaah.
The guideline concerning that is that whatever prevents water from reaching the skin means that wudoo’ is not valid, and whatever does not prevent water from reaching the skin means that wudoo’ is valid.
Based on this, wudoo’ is valid if there is ink on any part of the body that is washed in wudoo’, because it does not prevent water reaching the skin.
With regard to ghee, if it is solid and prevents water from reaching the skin, then it means that wudoo’ is not valid, but if what is left on the skin is just a trace, or it was liquid like oil, then wudoo’ is valid, but in this case you should make sure by rubbing the limb, because grease repels water. This has been explained in the answer to question no. 9493.
Al-Nawawi said in al-Majmoo’ (1/456):
If there is wax, dough, henna and the like on one of his limbs, which prevents water from reaching any part of it, then his tahaarah is not valid, whether the amount is large or small. If there are traces of henna and its colour left on the hand, without there being any solid material left, or elsewhere, or traces of liquid grease whereby water flows over the limb but does not stay there, his tahaarah is valid. End quote.
Solid secretions of the eye which may be in the inner corner of the eye must be removed according to some scholars. There is a da’eef hadeeth about wiping the inner corners of the eyes. This has already been discussed in the answer to question no. 45812.
With regard to earwax, whatever is on the outside of the ear must be removed, unlike that which is inside the ear. This has already been discussed in the answer to question no. 34172.
And Allaah knows best.